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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numeric_bindings.reference.blas"></a><a class="link" href="blas.html" title="BLAS"> BLAS</a>
</h3></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="blas/level_1_blas.html">Level
        1 BLAS</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="blas/level_1_blas/asum.html">asum</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/axpy.html">axpy</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/copy.html">copy</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/dotc.html">dotc</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/dot.html">dot</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/iamax.html">iamax</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/nrm2.html">nrm2</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/prec_dot.html">prec_dot</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/rotg.html">rotg</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/rot.html">rot</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/rotmg.html">rotmg</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/rotm.html">rotm</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/scal.html">scal</a></span></dt>
<dt><span class="section"><a href="blas/level_1_blas/swap.html">swap</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="blas/level_2_blas.html">Level
        2 BLAS</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="blas/level_2_blas/gbmv.html">gbmv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/gemv.html">gemv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/gerc.html">gerc</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/ger.html">ger</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/geru.html">geru</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/hbmv.html">hbmv</a></span></dt>
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<dt><span class="section"><a href="blas/level_2_blas/her.html">her</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/hpmv.html">hpmv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/hpr2.html">hpr2</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/hpr.html">hpr</a></span></dt>
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<dt><span class="section"><a href="blas/level_2_blas/spr2.html">spr2</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/spr.html">spr</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/symv.html">symv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/syr2.html">syr2</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/syr.html">syr</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/tbmv.html">tbmv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/tbsv.html">tbsv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/tpmv.html">tpmv</a></span></dt>
<dt><span class="section"><a href="blas/level_2_blas/tpsv.html">tpsv</a></span></dt>
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<dt><span class="section"><a href="blas/level_2_blas/trsv.html">trsv</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="blas/level_3_blas.html">Level
        3 BLAS</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="blas/level_3_blas/gemm.html">gemm</a></span></dt>
<dt><span class="section"><a href="blas/level_3_blas/hemm.html">hemm</a></span></dt>
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<dt><span class="section"><a href="blas/level_3_blas/syr2k.html">syr2k</a></span></dt>
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<dt><span class="section"><a href="blas/level_3_blas/trmm.html">trmm</a></span></dt>
<dt><span class="section"><a href="blas/level_3_blas/trsm.html">trsm</a></span></dt>
</dl></dd>
</dl></div>
<p>
        BLAS consists of three levels of routines:
      </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
            <span class="bold"><strong>level 1</strong></span> routines involve scalar-vector
            and vector-vector operations, like computing an inner product,
          </li>
<li class="listitem">
            <span class="bold"><strong>level 2</strong></span> routines cover vector-matrix
            operations, and
          </li>
<li class="listitem">
            <span class="bold"><strong>level 3</strong></span> routines perform matrix-matrix
            operations.
          </li>
</ul></div>
<div class="table">
<a name="boost_numeric_bindings.reference.blas.level_1_blas"></a><p class="title"><b>Table&#160;1.1.&#160;Level 1 BLAS</b></p>
<div class="table-contents"><table class="table" summary="Level 1 BLAS">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  BLAS
                </p>
              </th>
<th>
                <p>
                  Boost.Numeric_Bindings Equivalent
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  xROTG
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::create_rotation</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xROTMG
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::create_rotation</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xROT
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::apply_rotation</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xROTM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::apply_rotation</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSWAP
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::swap</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSCAL
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::scale</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xCOPY
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::copy</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xAXPY
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xDOT
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::dot</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xDOTU
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::dot</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xDOTC
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::dot</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xxDOT
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::dot</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xNRM2
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::norm_2</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xASUM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::abs_sum</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  IxAMAX
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::index_norm_inf</code>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_numeric_bindings.reference.blas.level_2_blas"></a><p class="title"><b>Table&#160;1.2.&#160;Level 2 BLAS</b></p>
<div class="table-contents"><table class="table" summary="Level 2 BLAS">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  BLAS
                </p>
              </th>
<th>
                <p>
                  Boost.Numeric_Bindings Equivalent
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  xGEMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xGBMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHEMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHPMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSYMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSBMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTRMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTBMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTPMV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTRSV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::forward_solve</code>,
                  <code class="computeroutput">blas::back_solve</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTBSV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::forward_solve</code>,
                  <code class="computeroutput">blas::back_solve</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTPSV
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::forward_solve</code>,
                  <code class="computeroutput">blas::back_solve</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xGER
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xGERU
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xGERC
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHER
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHPR
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHER2
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_2_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHPR2
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_2_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSYR
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSPR
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_1_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSYR
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_2_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSPR
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_2_update</code>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_numeric_bindings.reference.blas.level_3_blas"></a><p class="title"><b>Table&#160;1.3.&#160;Level 3 BLAS</b></p>
<div class="table-contents"><table class="table" summary="Level 3 BLAS">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  BLAS
                </p>
              </th>
<th>
                <p>
                  Boost.Numeric_Bindings Equivalent
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  xGEMM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSYMM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHEMM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSYRK
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_k_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHERK
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_k_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xSYR2K
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_2k_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xHER2K
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::rank_2k_update</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTRMM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::transform</code>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  xTRSM
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput">blas::forward_solve</code>,
                  <code class="computeroutput">blas::back_solve</code>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2002 -2009 Rutger ter Borg, Kre&#353;imir Fresl, Thomas Klimpel,
      Toon Knapen, Karl Meerbergen<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
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